S'7il THIRD REPORT— 1838. 



be physically exact, the ray which proceeds in the direction of 

 the line joining two opposite cusps on the wave-surface should 

 be refracted in every plane. This was accordingly found to be 

 the case. In the neighbourhood of each of the optic axes the 

 luminous line swelled out on either side of the plane of the 

 axes in an oval curve. This curve is the conchoid of Nico- 

 medes, whose asymptot is the line on the first surface ; and 

 its variations of form, as the plane passing through the two 

 apertures deviated from the plane of the optic axes, were highly 

 curious and remarkable. 



Examining the state of polarization of the rays composing 

 the emergent cone, Mr. Lloyd discovered that they observed 

 the following law, namely, that " the angle between the planes 

 of polarization of any two rays of the cone is half the angle 

 contained by the planes passing through the rays themselves 

 and its axis." This law, it is easy to show, is in perfect ac- 

 cordance with theory. 



Internal conical refraction should take place, according to 

 Professor Hamilton, when a single ray has been incident ex- 

 ternally upon a biaxal crystal in such a manner that one of the 

 refracted rays may coincide with an optic axis. The ray, in 

 this case, ought to be divided into a cone of rays within the 

 crystal, the angle of which in the case of arragonite is 1° 55'. 

 The rays forming this cone will be refracted at the second sur- 

 face of the crystal in directions parallel to the ray incident on 

 the first ; so that they will form a small cylinder of rays in air, 

 whose base is the section of the cone formed by the surface of 

 emergence. 



The minuteness of this phaenomenon, and the perfect accu- 

 racy required in the incidence, render it much more difficult of 

 detection than the former. A very fine I'ay of light proceeding 

 from a distant lamp was suffered to fall upon the crystal, and 

 the position of the latter altered with extreme slowness, so as 

 to change the incidence very gradually. When the required 

 position was attained, the two rays suddenly spread into a con- 

 tinuous circle, whose diameter was apparently equal to their 

 former distance. The same experiment was repeated with the 

 sun's light, and the emergent cylinder received on a small 

 screen of paper at various distances from the crystal. No sen- 

 sible enlargement of the section was visible on increasing the 

 distance. 



The magnitude of the angle of the cone of rays within the 

 crystal was ascertained experimentally, and agreed within very 

 narrow limits with that deduced from theory. The rays com- 

 posing the cone were all polarized in different planes, and the 



